Question

plz answer this question

Answer 1

Suppose 1 worker does 1 unit work in a day

Assume 150 workers can finish the work in (n-8) days, if all workers work all the days.
Then, total work =150(n−8) ⋯(1)=150(n−8) ⋯(1)
AP is 150,146,142,...
a = 150
d = -4
Sn = n/2[2×150+(n−1)(−4)]
=n/2[300−4n+4]=n2[304−4n]
=n(152−2n) ⋯(2)
From (1) and (2),
150(n−8)=n(152−2n)
75(n−8)=n(76−n)
75n−600=76n−n²
n²−n−600=0
(n−25)(n+24)=0
n=25 or n=-24
Therefore total no. of days required to complete the work is 25 days